A.A. Potapov, A.V. Strukov

Absence in the existing theory of numbers of mathematical apparatus allowing carrying out initial operations with new numbers on actual infinity creates a basis for necessity of working out of additions to the existing theory. The purpose of such additions is closing of existing blanks in operations with new numbers on infinity. An urgency of working out of additions it is connected by that the existing mathematical apparatus allows to see only an overall picture of processes arising on infinity. Detection of new numbers on actual infinity, and also operation with them is difficult processes of demanding big versatile knowledge in the mathematician, geometry, philosophy and metaphysics. And also process with the decision of many problems with a considerable quantity of unknown persons. Therefore for the decision of these problems on research problem statement, first of all, has been developed for generalization of all questions in one article which should be solved further for reception of the result put before research. Statement of problems on research has included four basic stages. The decision which will allow to come nearer on a step to disclosing of a curtain of secret of actual infinity.